thumb|400x400px|Comparison of the [[Big Bang concept (left) and a Hartle–Hawking state concept (right) as they are extrapolated to time zero. Diagram shows two space dimensions horizontally and one time dimension vertically.]]
The Hartle–Hawking state, also known as the no-boundary wave function, is a cosmological model that applies quantum mechanics to the Big Bang.
The concept can also be considered as an initial condition for models of quantum cosmology.
Ingredients
The Hartle-Hawking proposal includes several ingredients. First it uses Richard Feynman's path integral formulation of quantum mechanics. In this approach every possible path a particle can take through spacetime contributes to the solution with its own an amplitude and phase. Technical challenges with those sums lead to the second ingredient, a transformation to Euclidean space-time: a geometry which combines 3 space dimensions with an imaginary time dimension.
In 1998 Hawking worked with Neil Turok to expand the Hartle-Hawking concept to include a hyperbolic or open geometry.